Several methods are used for measuring surface profiles or contours of remote surfaces. For example, using optical interferometry, which provides highly accurate measurement of surface variations, coherent light is split into two beams. A first beam is radiated onto a target surface to be measured and the light that is reflected or reradiated from the surface is combined with a second beam that has a fixed optical path length between the source and the detector. The phase difference between the two beams is proportional to the difference in path lengths, modulo 2.pi.. If the light in the reradiated beam and the second beam are in phase, they will constructively interfere and the combination will appear bright. When the two beams are 180.degree. out of phase, they will destructively interfere and the resulting beam will appear dark. For a known wavelength .lambda. of light, optical detection of the phase difference by observation of light and dark areas can provide a measure of the depth of the irradiated spot.
However, optical interferometry is confounded by the phenomenon of speckle when the surface is optically rough. A surface is optically rough when the optical depth variance within a resolution cell gives a uniform phase probability distribution when reduced modulo 2.pi.. The return field from such a surface is thus the sum of a large number of unresolved point sources at different uniformly distributed random phases, and an interferometer will see the sum. This generally occurs where there are depth variations on the order of .lambda./4 over a length scale of .lambda.. The amplitude seen on an image plane spaced apart from the target surface has an exponential distribution, with highest probability for an unusable small value. One may consider the use of averaging over a finite region of the surface, but the lack of correlation in height on a scale of several wavelengths of the light prevents this. Moreover, the rough surface is resolved when the lateral scale of the roughness is larger than a resolution cell of the optical system viewing the surface as a source. When a surface is rough over the entire irradiated extent, the autocorrelation function of the optical depth determines the angular distribution of the reradiated energy. If the surface is uncorrelated, or only weakly correlated, the reradiated energy will be manifested by a random speckle irradiance pattern when projected on to a second surface spaced from the irradiated surface. The spatial frequency content of the reradiated energy is such that the use of conventional interferometry is further thwarted by the lack of a useful receiver solid angle, since the phase will only be slowly changing over the speckles.
For these reasons optical methods have projected interference patterns onto the surface or have used conventional resolution and stereovision techniques to profile surfaces.